Cyanobacteria are

The correct answer is oxygenic with nitrogenase.

Explanation:
1. Oxygenic Photosynthesis: Cyanobacteria (also known as blue-green algae) are photosynthetic prokaryotes. They are unique among bacteria because they perform oxygenic photosynthesis, using water ($H_{2}O$) as an electron donor and releasing oxygen ($O_2$) as a byproduct, similar to eukaryotic plants and algae.
2. Nitrogenase Enzyme: Many cyanobacteria are capable of fixing atmospheric nitrogen ($N_2$) into bioavailable forms like ammonia (${\mathrm{NH}}_3$). This process is catalyzed by the enzyme nitrogenase.
3. The Oxygen-Nitrogenase Paradox: Nitrogenase is highly sensitive to oxygen and is irreversibly inactivated by it. To protect nitrogenase from the oxygen produced during photosynthesis, cyanobacteria have evolved specialized mechanisms. For example, some species isolate nitrogenase in specialized, thick-walled cells called heterocysts, while others fix nitrogen only during the night when photosynthesis is inactive.
Therefore, cyanobacteria are characterized as being oxygenic organisms that possess the nitrogenase enzyme.